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Related Concept Videos

Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

213
Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
213
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

508
Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for...
508
Measurements of Strain01:27

Measurements of Strain

704
Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain...
704
Transformation of Plane Strain01:12

Transformation of Plane Strain

159
When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
159
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

264
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
264
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

183
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
183

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Related Experiment Video

Updated: Jun 24, 2025

Using Digital Image Correlation to Characterize Local Strains on Vascular Tissue Specimens
09:29

Using Digital Image Correlation to Characterize Local Strains on Vascular Tissue Specimens

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Radial basis point interpolation for strain field calculation in digital image correlation.

Jiayi Du, Jian Zhao, Jiahui Liu

    Applied Optics
    |June 10, 2024
    PubMed
    Summary

    A new Radial Basis Point Interpolation Method (RPIM) improves full-field strain calculation from noisy displacement data. This meshless approach offers enhanced computational efficiency and stability for accurate strain measurements, especially in areas with high strain gradients.

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    Area of Science:

    • Computational mechanics
    • Materials science
    • Experimental mechanics

    Background:

    • Digital Image Correlation (DIC) often yields noisy displacement fields.
    • Extracting accurate strain fields from noisy data is crucial for material analysis.
    • Existing methods like Element-Free Galerkin (EFG) face challenges with speed and stability.

    Purpose of the Study:

    • Introduce a Point Interpolation Meshless (PIM) method using Radial Basis Functions (RBF) for strain calculation.
    • Overcome limitations of traditional methods in speed and matrix inversion stability.
    • Evaluate the performance of the proposed method against existing techniques.

    Main Methods:

    • Developed a Radial Basis Point Interpolation Method (RPIM) for full-field strain calculation.
    • Compared RPIM with Moving Least Squares (MLS) and Pointwise Least Squares (PLS) methods.
    • Validated strain fields with high gradients using simulation experiments and different RBFs (e.g., Multiquadric).

    Main Results:

    • RPIM demonstrated significant computational efficiency gains over MLS (up to 80%).
    • RPIM showed improved calculation stability and robustness against displacement noise and support domain size.
    • RPIM achieved comparable accuracy to MLS (0.3-0.5% difference) and outperformed PLS in noise insensitivity.

    Conclusions:

    • The proposed RPIM offers a robust and accurate alternative for full-field strain calculation.
    • RPIM is particularly effective for analyzing strain fields with high gradients, such as at crack tips.
    • The method provides a practical approach for experimental mechanics and material characterization.